Johnston played both baseball and basketball at Chillicothe HS and then at Ohio State. He left school early to pursue baseball, pitching in the Philles farm system from 1949-1951. After pitching for Wilmington in the Interstate (B) League in 1951, his manager Jim Ward helped him get a tryout with the Philadelphia Warriors. He made the team, and never looked back to the mound. Blessed with a sweet hook shot, Johnston played 8 seasons with the Warriors, leading the league in shooting percentage multiple times and also in rebounded. (He also got a Masters Degree at Temple during this time.) In 1959, he severely injured his knee and moved from the court to the bench, coaching the Warriors for 2 seasons. He moved over the the Pittsburgh Rens of the new ABL in 1961, and was a player / coach. He quite playing but stayed on the bench in the next season, and the ABL folded after the 62-63 season. After a year off, Johnston coached Wilmington in the Eastern League for a couple seasons before Jack McCloskey hired him as his assistant at Wake Forest. Six years later, McCloskey left for the NBA, and Johnston was not hired by Wake to replace him, and instead fired him. McCloskey brought him on board at Portland. They were both fired after two seasons there. Johnston took a job with the BBB in Portland before returning to basketball in 1976 as the head coach at Chemetka CC in Salem, Oregon. After one season there, he was offered the Athletic Director job at North Lake Community College in Irving Texas in the summer of 1977.

On one warm September day in 1978, Johnston was playing basketball with some friends and family when he collapsed. The heart attack he was suffering would prove to be fatal. He was only 49 years old. He was posthumously elected to the National Basketball Hall of Fame in 1990.

Neil married Phyllis Wilson (1931-1980) and they had two sons and three daughters.